Active Streamable HTTP sessions are not terminated during shutdown

Initial Checks

• I confirm that I'm using the latest version of MCP Python SDK
• I confirm that I searched for my issue in https://github.com/modelcontextprotocol/python-sdk/issues before opening this issue

Description

Context

This is primarily a repost of this fastmcp issue as it seems to actually be a bug in the mcp python sdk and I want to make sure we've got visibility over here.

When shutting down a FastMCP server (CTRL+C) while clients have active streaming connections, Uvicorn logs:

ERROR: ASGI callable returned without completing response.

The error occurs because StreamableHTTPSessionManager cancels the task group without first gracefully terminating active SSE/streaming connections.

Expected behavior would be the active connections being closed with a proper http response before the rest of shutdown.

Example Code

from fastmcp import FastMCP

mcp = FastMCP("Test Server")

@mcp.tool
def hello() -> str:
  return "Hello, World!"

if __name__ == "__main__":
  mcp.run(transport="streamable-http", port=8000)

Python & MCP Python SDK

Python 3.12
MCP Python SDK 1.26.0

Comienza con el manejo del shutdown de StreamableHTTPSessionManager y reproduce el problema usando el ejemplo streamable-http con Python 3.12. Traza cómo se cancelan las conexiones SSE o de streaming activas y, a continuación, verifica que el shutdown las cierre con una respuesta HTTP adecuada sin el error de Uvicorn ASGI.